{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T20:43:37Z","timestamp":1649018617067},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"supp02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2007,4]]},"abstract":"<jats:p> A fundamental problem in fuzzy analysis is that the membership function is specified subjectively. In other words, the modelers specify the membership function form and assign the values of the parameters in membership function via their working experiences. Different from its probabilistic counterpart, fuzzy mathematical theory does not provide convenient parameter estimation approach. In this paper, we first review Liu's non-classical credibility measure theory (i.e., (\u2228,\u00b7)-credibility measure theory) in Liu<jats:sup>7<\/jats:sup>, because the fuzzy theory initiated by Zadeh<jats:sup>10<\/jats:sup> contains a critical weakness: non self-duality property for possibility measure. We establish a parameter estimation of the membership function in terms of maximum entropy principle on the ground of self-dual credibility measure theory. Furthermore, based on the data assimilated membership function, we can calculate membership grades on the fuzzy environmental index, using PM<jats:sup>10<\/jats:sup> air pollution as an illustration. We treat the calculated membership grades as spatially distributed random quantity, and therefore perform the standard ordinary kriging approach for generating the predicted environmental index map, for PM<jats:sup>10<\/jats:sup> prediction map. <\/jats:p>","DOI":"10.1142\/s0218488507004601","type":"journal-article","created":{"date-parts":[[2007,5,21]],"date-time":"2007-05-21T07:43:34Z","timestamp":1179733414000},"page":"53-66","source":"Crossref","is-referenced-by-count":0,"title":["CREDIBILITY MEASURE-BASED FUZZY MEMBERSHIP GRADE KRIGING"],"prefix":"10.1142","volume":"15","author":[{"given":"DANNI","family":"GUO","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences, University of Cape Town, Private Bag, Rhodes' Gift, Rondebosch 7701, Cape Town, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RENKUAN","family":"GUO","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Cape Town, Private Bag, Rhodes' Gift, Rondebosch 7701, Cape Town, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHRISTIEN","family":"THIART","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Cape Town, Private Bag, Rhodes' Gift, Rondebosch 7701, Cape Town, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf4","volume-title":"Introduction to the Theory of Fuzzy Subsets","author":"Kaufmann A.","year":"1975"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-39987-2"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-006-0016-x"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(72)90199-4"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90029-5"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488507004601","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:12:23Z","timestamp":1565133143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488507004601"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,4]]},"references-count":6,"journal-issue":{"issue":"supp02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2007,4]]}},"alternative-id":["10.1142\/S0218488507004601"],"URL":"https:\/\/doi.org\/10.1142\/s0218488507004601","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,4]]}}}